Problem: Solve for $k$, $ -\dfrac{9}{2k - 1} = -\dfrac{9}{2k - 1} - \dfrac{k + 4}{6k - 3} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $2k - 1$ $2k - 1$ and $6k - 3$ The common denominator is $6k - 3$ To get $6k - 3$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ -\dfrac{9}{2k - 1} \times \dfrac{3}{3} = -\dfrac{27}{6k - 3} $ To get $6k - 3$ in the denominator of the second term, multiply it by $\frac{3}{3}$ $ -\dfrac{9}{2k - 1} \times \dfrac{3}{3} = -\dfrac{27}{6k - 3} $ The denominator of the third term is already $6k - 3$ , so we don't need to change it. This give us: $ -\dfrac{27}{6k - 3} = -\dfrac{27}{6k - 3} - \dfrac{k + 4}{6k - 3} $ If we multiply both sides of the equation by $6k - 3$ , we get: $ -27 = -27 - k - 4$ $ -27 = -k - 31$ $ 4 = -k $ $ k = -4$